Abstract
An approach for the reconstruction of the velocity field in ideal atmospheric dynamics for given density and the two tracers potential vorticity and potential temperature (entropy) is presented. The method is based on the fundamental equations without approximation. The key step is to satisfy the continuity equation by the inclusion of a third Lagrangian tracer χ. This field is determined by closure conditions for density, potential vorticity and by boundary conditions. The reconstruction is, using the exterior calculus, with the four-dimensional 1-form based on the velocity components (1, u, v, w), density , potential vorticity Q and potential temperature θ. In the mean atmospheric flow χ represents the initial longitude of a fluid particle. For stationary flows χ is related to the Bernoulli function. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flow.
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